Answer:
To determine when Chase should sell the car, we need to calculate how many years it will take for the car's value to reach $20,000.
Given that the car loses 15% of its value each year, we can use the formula:
f(x) = 55,500 * (1 - 0.15)^x
where x represents the number of years.
To find when the car's value reaches $20,000, we need to solve the equation:
20,000 = 55,500 * (1 - 0.15)^x
To simplify, let's rewrite the equation using 0.85 as the decimal representation of (1 - 0.15):
20,000 = 55,500 * 0.85^x
Now, we need to solve for x. To do this, we can take the logarithm of both sides of the equation:
(20,000) = (55,500 * 0.85^x)
Using logarithm properties, we can rewrite the equation as:
(20,000) = (55,500) + (0.85^x)
Applying the power rule of logarithms, which states that (a^b) = b * (a), we get:
(20,000) = (55,500) + x * (0.85)
Now, we can substitute the values of (20,000) and (55,500), which are approximately 4.301 and 4.743, respectively:
4.301 = 4.743 + x * (0.85)
Simplifying the equation:
-0.442 = x * (0.85)
Dividing both sides by (0.85):
x = -0.442 /(0.85)
Using a calculator, we find that x is approximately 5.264.
Therefore, Chase should sell the car after approximately 5 years to reach a value of $20,000.
In the given options, the correct answer is:
- Sell the car after 5 years.